NEW YORK — June sales heated up for stores, in a sign that Americans likely will continue to spend during the important back-to-school shopping season.

U.S. retailers reported their strongest sales gains since January, as shoppers, enticed by warm weather and an improving economy, took advantage of summer discounts.

Revenue at stores opened at least a year — an industry measure of a retailer’s health — rose 3.9 percent in June compared with the same month a year ago, according to a preliminary tally of 12 retailers by the International Council of Shopping Centers. The mall trade group had expected an increase of 3 to 3.5 percent.

The data, released Thursday, offers positive signs for the back-to-school season, which is the second-biggest shopping period behind the winter holidays. June is when stores clear out summer merchandise to make room for goods for fall, so brisk sales mean that stores likely won’t be stuck with piles of summer shorts and T-shirts that they need to get rid of as the back-to-school kicks off later this month.

June’s performance was its best performance since January’s 4.5 percent gain and showed a gradual improvement since early this spring. The tally was up 3.4 percent in May and 3 percent in April.

Going forward, Michael P. Niemira, chief economist at the International Council of Shopping Centers, expects that total sales for the back-to-school season, which runs from mid-July through mid-September, will be up a solid 3.1 percent to $42.2 billion. That would be less than the 3.6 percent gain in 2011, but in line with the 3.3 percent pace on average over the past 10 years.

Stores are benefiting from an improving economy that has gained a robust 195,000 jobs in June. Employers have added an average 202,000 jobs for the past six months, up from 180,000 in the previous six. The housing market is also gaining strength. And consumer confidence in June is at the highest level since January 2008, according to the Conference Board.

“The reports are encouraging,” Niemira said. “We had seen consumers pull back a littler earlier this year, but now there’s a willingness to spend. It adds to the flavor of the other economic data out there that looks better.”

Indeed, while big chains such as Wal-Mart Stores, Target Corp. and Macy’s Inc. no longer report monthly revenue, the stores that do offer economists a snapshot of consumer spending habits. In total, the retailers that report monthly data represent about 6 percent of the $2.4 trillion in U.S. retail industry sales.

One of the retailers that reported monthly revenue is Stein Mart, a department store chain that sells everyday low prices on top brands. The retailer said June revenue at stores open at least a year climbed 6.5 percent, driven by strong sales of women’s clothing. Analysts had expected a 4 percent increase.

Costco Wholesale Corp. also was among the retailers that posted a revenue increase in June. The wholesale-club operator said revenue at stores open at least a year climbed 6 percent, topping Wall Street’s expectations. Analysts surveyed by Thomson Reuters predicted a 5.4 percent increase in the figure.

For instance, Jamie Achilli, a mother who lives in Carrollton, Tex., has been taking advantage of deals at Kohl’s Corp. Among the bargains she grabbed were $4 yoga pants originally priced at $20. She also bought tops for $2 for her two-year old daughter.

“I loaded up on clothes for myself,” said Achilli, 35. “I waited until they went to 80 percent clearance.”

Dan Granger, 41, from Peters, Missouri, also said he’s remained frugal because he’s still digging himself out of from the Great Recession. He and his family are renting a condominium after losing their home, and he had been unemployed for two years before finding a job as a maintenance manager for a commercial real estate company in February 2012.

So, Granger took advantage of deals for himself last month. He also got a head start on back-to-school shopping for his sons, ages 13 and 17 and bought them discounted summer clothes that they can wear in September. Overall, he spent about $600, but he said he will wait for another end-of-the-season sale to buy more.

“In this economy, you have to get deals where you can,” Granger said. “We’re starting over like 18-year-olds.”

Analysts expect that stores are going to have to continue to offer discounts heading into the back-to-school shopping season to meet the needs of deal-hungry shoppers. In fact, department store chain Kohl’s Corp. is already discounting school uniforms anywhere from 30 percent to 35 percent and certain backpacks from 20 percent to 40 percent.

“Retailers are going to be quite promotional,” said Madison Riley, managing director at Kurt Salmon.